The actual chemistry of what happens is far more complex than what you describe. We try not to get into too much detail here on this forum except in The Deep End. Chlorine doesn't just kill organisms by oxidation of certain chemicals and that isn't the initial way that most pathogens get killed. The chlorine can also kill them by attaching to critical molecules usually in a substitution reaction where it replaces a hydrogen attached to a nitrogen (in an amine). This then makes some protein chemicals not work properly anymore usually by causing them to either unfold or to clump together (depending on the protein and where it is attacked). The microorganism then goes into a shock similar to what happens when you apply too much heat since that also disrupts protein chemistry.
This article talks about how bleach kills bacteria (you can read
this paper for even more details).
MPS is a more selective oxidizer in some ways and it doesn't do the substitution reaction so tends to cause less havoc inside cells. Of course, everything is concentration dependent, but I'm talking about the usual ppm concentrations used for these chemicals.
Silver kills bacteria not through oxidation reactions but by binding to sulfur in proteins preventing them from folding properly. Silver also interferes with iron metabolism since iron is bound in some reactions by sulfur.
This article talks about the process (
this paper goes into more detail). However, metal ions such as copper and silver, do not kill as quickly as chlorine for most pathogens. This is described in
this post where you can see that silver ions kill fecal bacteria around 50 or more times as slowly as chlorine whereas copper ions don't kill such bacteria at all (again, at pool concentrations) because such bacteria live in the G.I. tract that is exposed to bodily fluids that already contain copper so these organisms have mechanisms for removing or sequestering copper to prevent it from damaging them. Copper is better at inhibiting algae growth because the algae don't have copper-resistant mechanisms like fecal bacteria and algae reproduce more slowly so the slow killing isn't as problematic.
The silver ions with MPS at hot temperatures are different since they create sulfate free radicals and these are more destructive. Also, the created divalent silver ions are likewise more potent than regular silver ions.
We don't recommend the use of metal ions because of their risk of staining, especially for plaster surfaces.